What is the meaning of least squares in a regression model?
DEFINITION of 'Least Squares' Least squares is a statistical method used to determine a line of best fit by minimizing the sum of squares created by a mathematical function. A "square" is determined by squaring the distance between a data point and the regression line.
Visualizing the Hidden ‘Logic’ of Cities
David Montgomery
Jul 26, 2018
The trapezoidal rule and Simpson's rule.
Simpson's rule is a Newton-Cotes formula for approximating the integral of a function using quadratic polynomials (i.e., parabolic arcs instead of the straight line segments used in the trapezoidal rule).
The trapezoidal rule and Simpson's rule
Doh!
ConsumerTheory
The Consumer Problem
The Structure of Applied General Equilibrium Models
By Victor Ginsburgh, Michiel Keyzer
In microeconomics, a consumer's Marshallian demand function (named after Alfred Marshall) specifies what the consumer would buy in each price and income or wealth situation, assuming it perfectly solves the utility maximization problem.
Another Marshallese song to guide navigation include the lyrics 'lum-lum Enewetak Ak Eo!' which translates to English song lyrics as 'when you see the sands beneath water start to shine, you know you have gone to far north!' My neighbor is from the Marshall Islands and his great grandfather was Kai BooKee, the highest chief, his father served in WWii in Guadalcanal in the Army and he worked for a government contractor called the Transport Company of Texas in the 1960's as well with other government contractors between the 1960's and 1990's. His cousin was a former president of the Marshall Islands. He has helped me to a measurable degree with my research as a Small Business of Innovation Research, certified with the US as well as Texas HUB and Austin MBE, doing business as Serenity Sells.
Aunty's matter!
Costs
The Globalization of Markets
Word to my cousin Ray.
The Marshallese expression 'unare peim' translates as 'heap the labors of your hands' or reap what you sow. Thanks neighbor Andrew.
Marshallian and Hicksian demands
Why is Hicksian demand steeper than marshallian?
The Hicksian demand is steeper than the Marshallian Demand because the Hicksian Demand only accounts for substitution effects while the Marshallian Demand focuses on income and substitution effects.
Quantifying the supply‐side benefits from forward contracting in wholesale electricity markets
applied as
Optimal Supply Functions in Electricity Markets with Option
Contracts and Non-Smooth Cost
Vector fields
Electromagnetic field and continuous and differentiable vector fields
'As you sow so shall you reap' (differentiable vector fields)
as a
Random walk in a color of law case
Trump Finally Admits His Campaign Colluded With Russia At Trump Tower Meeting
The latest version of the 2016 meeting with a Kremlin-linked lawyer basically undercuts numerous Trump claims.
The Fields Medal is a prize awarded to two, three, or four mathematicians under 40 years of age at the International Congress of the International Mathematical Union (IMU), a meeting that takes place every four years.
Medal known as "Nobel for mathematics" stolen minutes after awarded to refugee
The Fields Medal is widely regarded as the highest honor a mathematician can receive, and has been described by many as the mathematician's "Nobel Prize".
Who is Akshay Venkatesh? Indian-origin man who won Fields Medal, the ‘Nobel for Mathematics’
Born in New Delhi, Akshay Venkatesh is an Indian-origin Australian mathematician who was among the four winners of the prestigious Fields Medal for Mathematics, also known as the Nobel prize for Math.
Fields Medals Awarded to 4 Mathematicians
Whom may solve for:
Russian journalists slain while investigating Kremlin-linked company in Central African Republic
Between 1870 and 1913 American rent rose by 248.9% while british rent fell 43.3%
The Drunkard’s Walk Explained
Stochastic Processes, Markov Chains & Random Walks
Real Estate
The End of the Global Housing Boom
After a years-long surge in global capitals, property prices are starting to head lower. From Sydney to Toronto, here’s a look at what’s ahead.
The Heckscher-Ohlin Trade Model
There are many statistical measures that show how productive the U.S. is.
Here's How America Uses Its Land
By Dave Merrill and Lauren Leatherby
July 31, 2018
The Calumet and Hecla Mining Company was a major copper-mining company based within Michigan's Copper Country. In the 19th century, the company paid out more than $72 million in shareholder dividends, more than any other mining company in the United States during that period.
Economics
What Economists Still Don’t Get About the 2008 Crisis
The general public might understand what causes busts better than the wonks.
A Nation of Drunkards
PROHIBITION
Local Option Alcohol Laws in the US: History & Status
A RAGING and bizarre family fight is buffeting the Sarah C. Getty Trust, the chief beneficiary of last year’s sale of Getty Oil to Texaco. At stake is control of about $4 billion in assets that, even after huge capital gains taxes, will still stack up at around $3 billion.
The War Between the Gettys
He sings the bravura aria of his part hesitantly, reluctantly and unwillingly, as though apologizing for being compelled by circumstance to "act the lion"
The American Presidents From Polk to Hayes: What They Did, What They Said ...
By Robert A. Nowlan, Ph.D.
Role of the Massachusetts Textile Mills in the Industrial Revolution
Lincoln's Selected Writings (International Student Edition) (Norton Critical ...
He sings the bravura aria of his part hesitantly, reluctantly and unwillingly, as though apologizing for being compelled by circumstance to "act the lion"
By Abraham Lincoln
The Heckscher–Ohlin model (H–O model) is a general equilibrium mathematical model of international trade, developed by Eli Heckscher and Bertil Ohlin at the Stockholm School of Economics. It builds on David Ricardo's theory of comparative advantage by predicting patterns of commerce and production based on the factor endowments of a trading region. The model essentially says that countries export products that use their abundant and cheap factors of production, and import products that use the countries' scarce factors.
'Liberty Cabbage', and Anti-German Sentiment
Because of this perceived conflict of loyalties, the Wilson administration was convinced that it had to mobilize public opinion in support of the war. To influence public opinion, the federal government embarked on its first ever domestic propaganda campaign.
Behind the Spectacular Collapse of a Private Equity Titan
Arif Naqvi rode Dubai’s rise to build Abraaj Group with an unusual business model. Was it a house of cards?
Trade, Growth, and Convergence in a Dynamic Heckscher-Ohlin Model
Critical Theory of Legal Revolutions: Evolutionary Perspectives
He sings the bravura aria of his part hesitantly, reluctantly and unwillingly, as though apologizing for being compelled by circumstance to "act the lion"
By Hauke Brunkhorst
The Heckscher-Ohlin (H-O; aka the factor proportions) model is one of the most important models of international trade.
Articles by Karl Marx in Die Presse 1862
Comments on the North American Events
The Civil War: The Second American Revolution
Green Lease Leadership meet Grassroots Leadership
The German word Hamburger, literally meaning "from the city of Hamburg," begins to appear on American menus in the late 1800s during a period of heavy German immigration.
What is liberty cabbage?
During World War I, due to concerns the American public would reject a product with a German name, American sauerkraut makers relabeled their product as "Liberty Cabbage" for the duration of the war. Want some Freedom Fries with that Liberty Sandwich?
What is the Liberty sandwich again Popeye?
A sandwich made with a patty of ground meat usually in a roll or bun. [Short for Hamburger steak, after Hamburg.] Word History: The German word Hamburger, literally meaning "from the city of Hamburg," begins to appear on American menus in the late 1800s during a period of heavy German immigration.
What would Homer from the Simpsons say?
(/doʊʔ/) is a catchphrase used by the fictional character Homer Simpson, from one of the longest running American animated sitcom The Simpsons (1989–present). It is typically used when Homer injures himself, realizes that he has done something stupid, or when something bad has happened or is about to happen to him
In mathematics, the modular group is the projective special linear group PSL(2,Z) of 2 x 2 matrices with integer coefficients and unit determinant. The matrices A and -A are identified. The modular group acts on the upper-half of the complex plane by fractional linear transformations, and the name "modular group" comes from the relation to moduli spaces and not from modular arithmetic.
In abstract algebra, the sedenions form a 16-dimensional noncommutative and nonassociative algebra over the reals obtained by applying the Cayley–Dickson construction to the octonions. Unlike the octonions, the sedenions are not an alternative algebra. It is possible to apply the Cayley-Dickson construction to the sedenions infinitely on, but the algebras created have the same properties as sedenions and are of little interest.
The term sedenion is also used for other 16-dimensional algebraic structures, such as a tensor product of two copies of the biquaternions, or the algebra of 4 by 4 matrices over the reals, or that studied by Smith (1995).
In mathematics, the Cayley–Dickson construction, named after Arthur Cayley and Leonard Eugene Dickson, produces a sequence of algebras over the field of real numbers, each with twice the dimension of the previous one. The algebras produced by this process are known as Cayley–Dickson algebras, for example complex numbers, quaternions, and octonions. These examples are useful composition algebras frequently applied in mathematical physics.
The Cayley–Dickson construction defines a new algebra similar to the direct sum of an algebra with itself, with multiplication defined in a specific way (different from the multiplication provided by the genuine direct sum) and an involution known as conjugation. The product of an element and its conjugate (or sometimes the square root of this product) is called the norm.
The symmetries of the real field disappear as the Cayley–Dickson construction is repeatedly applied: first losing order, then commutativity of multiplication, associativity of multiplication, and next alternativity.
More generally, the Cayley–Dickson construction takes any algebra with involution to another algebra with involution of twice the dimension.
trigintaduonion
Noun
trigintaduonion (plural trigintaduonions)
trigintaduonion... what a weird fighting word, huh?
(mathematics) A 32-dimensional hypercomplex number that is a nonassociative extension of a sedenion.
A trigonometric equation is one in which the unknown to be solved for is an angle (call it θ) and that angle is in the argument of a trigonometric function such as sin, cos or tan.
What is the argument in math?
In mathematics, an argument of a function is a specific input in the function, also known as an independent variable. When it is clear from the context which argument is meant, the argument is often denoted by the abbreviation arg.
In mathematics, Dedekind cuts, named after German mathematician Richard Dedekind, are а method of construction of the real numbers from the rational numbers. A Dedekind cut is a partition of the rational numbers into two non-empty sets A and B, such that all elements of A are less than all elements of B, and A contains no greatest element. The set B may or may not have a smallest element among the rationals. If B has a smallest element among the rationals, the cut corresponds to that rational. Otherwise, that cut defines a unique irrational number which, loosely speaking, fills the "gap" between A and B. In other words, A contains every rational number less than the cut, and B contains every rational number greater than or equal to the cut. An irrational cut is equated to an irrational number which is in neither set. Every real number, rational or not, is equated to one and only one cut of rationals.
Dedekind cuts can be generalized from the rational numbers to any totally ordered set by defining a Dedekind cut as a partition of a totally ordered set into two non-empty parts A and B, such that A is closed downwards (meaning that for all a in A, x ≤ a implies that x is in A as well) and B is closed upwards, and A contains no greatest element. See also completeness (order theory).
It is straightforward to show that a Dedekind cut among the real numbers is uniquely defined by the corresponding cut among the rational numbers. Similarly, every cut of reals is identical to the cut produced by a specific real number (which can be identified as the smallest element of the B set). In other words, the number line where every real number is defined as a Dedekind cut of rationals is a complete continuum without any further gaps.
A similar construction to that used by Dedekind cuts was used in Euclid's Elements (book V, definition 5) to define proportional segments.
In mathematics, a hypercomplex number is a traditional term for an element of a unital algebra over the field of real numbers. The study of hypercomplex numbers in the late 19th century forms the basis of modern group representation theory.
Show your proof kids...
A COURSE IN ABSTRACT ALGEBRA
"I'll gladly pay you Tuesday for a hamburger today."
Doh!